Fast Algorithm for Computing the Upper Endpoint of Sample Variance for Interval Data: Case of Sufficiently Accurate Measurements

Authors

Gang Xiang

Publication Date

3-2005

Comments

Technical Report: UTEP-CS-04-31a.

Published in Reliable Computing, 2006, Vol. 12, No. 1, pp. 59-64.

Abstract

When we have n results x1,...,xn of repeated measurement of the same quantity, the traditional statistical approach usually starts with computing their sample average E and their sample variance V. Often, due to the inevitable measurement uncertainty, we do not know the exact values of the quantities, we only know the intervals [xi] of possible values of xi. In such situations, for different possible values xi from [xi], we get different values of the variance. We must therefore find the range [V] of possible values of V. It is known that in general, this problem is NP-hard. For the case when the measurements are sufficiently accurate (in some precise sense), it is known that we can compute the interval [V] in quadratic time O(n^2). In this paper, we describe a new algorithm for computing [V] that requires time O(n log(n)) (which is much faster than O(n^2)).